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Mathematics > Algebraic Geometry

Abstract: Let $f$ be an invertible polynomial and $G$ a group of diagonal symmetries of
$f$. This note shows that the orbifold Jacobian algebra $\mathrm{Jac}(f,G)$ of
$(f,G)$ defined by the authors and Elisabeth Werner in arXiv:1608.08962 is
isomorphic as a $\mathbb{ZZ}/2\mathbb{ZZ}$-graded algebra to the Hochschild
cohomology $\mathsf{HH}^*(\mathrm{MF}_G(f))$ of the dg-category
$\mathrm{MF}_G(f)$ of $G$-equivariant matrix factorizations of $f$ by
calculating the product formula of $\mathsf{HH}^*(\mathrm{MF}_G(f))$ given by
Shklyarov in arXiv:1708.06030. We also discuss the relation of our previous
results to the categorical equivalence.